How to show exact answers when using the "residue(a,b)" command

I have this math problem in which I am trying to expand a rational function of the form into something that looks like this:

where the numerators and p are constants. To take an example, I have the following function and when I tried to expand this manually, I found this result:

Now, that was a relatively easy example and I may need MATLAB in order to quicken my calculations when I deal with higher order denominators and the function residue() allows that. In the console, I tried this:

>>N = [2];
>>D = [1 12 36 0];
>>[r p y] = residue(N,D)
r =
-0-0556
-0.3333
0.0556

p=
-6
-6
0

y=
[]

Now, the solution found by residue() certainly agrees with the one I found manually, but I need exact not numerical solutions with decimal points. I was searching on the forum before asking my question, then found this thread. Basically, it suggests to use symbolic arithmetic with the sym command.

Therefore, I tried to proceed as such but the residue() command only accepts inputs which are floats. Here is the error message I received:

Answer 1

[Star Strider]

This is a partial fraction expansion (decomposition), so use the partfrac function (introduced in R2015a):

syms s V(s) 
V = 2/(s^3 + 12*s^2 + 36*s)
Vpf = partfrac(V)
pretty(Vpf)

producing:

.

[billyandriam]

This accurately solves my issue; thank you vey much!

[Star Strider]

As always, my pleasure!